Effect of the actions do not appear immediately - the behaviour evolves with time
Eg. To go from 30 km/hr to 60 km/hr in a car we press the accelerator pedal. We know the card doesn't reach 60 km/hr immedately, it takes a few seconds to accelerate to that velocity.
Mathematical Representation of a physical, biological or information system. In this class, we focus on dynamical systems (mostly in state-space form)
"All models are wrong, but some are useful". Often, a model is an approximation of the real system. The real system might be too complicated to model perfectly. For eg. aerodynamic interactions between the rotor blades of a quadcopter, friction between the tire and ground for a physical robot etc.
The required modelling accuracy depends on the application at hand. Eg. aerodynamic drag can be neglected for low-speed control design for quadcopters
Analysis and design must performed keeping in mind the limitations of the model
Simulation
Controller design
Verfication and Validaton
Diagnostics, predictive maintenance
Equation is:
\[ \tau\dot{x} + x = u(t) \]For damping ratio close to 1, it can be approximated as
\[ \ddot{x} + \frac{2\zeta\dot{x}}{\tau} + \frac{x}{\tau^2} = u(t) \].The settling time is around 4 time constants